. oi 
r, {1 ate ‘a se fesed) = + cot dy \ ae {a + f ese ba + cot ooh 
= oO) ah OR ee 0 eee 
R(1 + fese go) » 
cot Po 
2 
[22 j 
Similarly solving Equation [11] for functions of ¢ we obtain the 
following formulas for T, s, and y. 
Y= 
1+ fa + fese dame oP ese bo) 
isle o = 
Re 
1 + fesedo Tt s (al [25] 
; 2 i 
{a + PC) ee + ese bo| - i} — cotdo 
p= Dy [24] 
R 1+ fesce do 
1 
‘ i 
r {{o “F Gece + ese by| x iS + (1 + feseds) + ese, 
a In ui 
R(1 + fese do) ane Po 
: [25] 
Thus when the cable parameters F and R and complete conditions are 
given at any one point, complete conditions can be found at once for any other 
point at which one value is known. 
Usually these points are the downstream 
and upstream ends of the cable respectively. 
Greater difficulty is presented by problems which do not specify all 
the cable parameters or complete conditions at any one point. These problems 
can be treated by the methods described in Reference (4). 
If we define 
Tg eel CSC) 
[26] 
o = cot d [27] 
B= essey = il [28] 
Ao nen & 
9 [29] 
and let T), 49, € 9, and mM) be the values of these functions for ¢ = ¢» then 
from Equations [7], [9], [11], and [13] 
[30] 
